Paper: using HFD to get a good understanding of the relationships between the Covid-19 measurements and the other covariates. we did this by breaking the signal down into two components. (1) the trend of the data. This is created using a loess smoothing. (2) the detrended data. This captures the noise processes. furthermore there is two views of the data. We look at the normal data and the log of data. The log of the data better captures the shape of Wastewater and its noise. at the bottom of the document contain plots showing a comprehensive view of the problem. The main goal of this document is to show the main takeaways of those plots in an easier way to see. The main takeaways are, 1) the covariates don’t relate to the covid signal any more than the population does. 2) Crp and HF183 do relate strongly on the unlogged data. 3) Crp and HF183 are strongly related.

The table below shows the correlation between the Covid-19 signals and the covariate components. The baseline these covariates are meant to control for is population so Let’s first look at that. We can see in the original data it has a low correlation but in the log data it has a .3 correlation which is meaningful. This is larger then most of the covariates correlation which suggests that at least when working with the log of the data covariates other than population are not necessary. With the original data the HF183 and CrP have correlation of .3 which might be worth understanding. None of the detrended data correlates meaningful supporting the view that they are mostly caused by noise.

## # A tibble: 7 × 5
##   term            log_N1_Trend log_N2_Trend  N1_Diff N2_Diff
##   <chr>                  <dbl>        <dbl>    <dbl>   <dbl>
## 1 pop                  0.234        0.288    0.00155 -0.0119
## 2 log_PMMOV_Trend      0.213        0.171   -0.0170  -0.0133
## 3 log_HF183_Trend      0.287        0.227   -0.00854 -0.0258
## 4 log_CrP_Trend        0.211        0.179   -0.00868 -0.0178
## 5 PMMOV_Diff           0.0785       0.0755   0.00312  0.0163
## 6 HF183_Diff          -0.0247      -0.0265   0.0807   0.0613
## 7 CrP_Diff            -0.00671     -0.00292  0.0279   0.0295
## # A tibble: 7 × 5
##   term        N1_Trend N2_Trend    N1_Diff  N2_Diff
##   <chr>          <dbl>    <dbl>      <dbl>    <dbl>
## 1 pop           0.0659   0.119   0.0000270 -0.0253 
## 2 PMMOV_Trend   0.0654   0.0580 -0.000285   0.00341
## 3 HF183_Trend   0.365    0.371  -0.0214    -0.0640 
## 4 CrP_Trend     0.328    0.332  -0.0275    -0.0466 
## 5 PMMOV_Diff    0.0190   0.0112 -0.00669   -0.00436
## 6 HF183_Diff   -0.0134  -0.0230  0.00220   -0.00223
## 7 CrP_Diff     -0.0269  -0.0372  0.00290    0.0551

looking at the relationship between HF183 and CrP you see a distinctly strong relationship in both the trend and the noise. We don’t have enough understanding of the underlying process to know if this is expected.

##                    log      base
## trend corr   0.8801775 0.7616367
## detrend corr 0.4324156 0.1648089

For a baseline we showed the relationship between N1 and N2 that show an extremely strong correlation clearly due to them measuring the same thing.

##                    log      base
## trend corr   0.9268483 0.9824389
## detrend corr 0.3407199 0.3446168